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Nitrogen $\left( I \right)$ Oxide is produced by:
A.Thermal decomposition of ammonium nitrate
B.Disproportion of ${N_2}{O_4}$
C.Thermal decomposition of ammonium nitrite
D.Interaction of hydroxylamine and nitrous acid

Answer
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Hint: Usually oxides of nitrogen are a mixture of gases that are composed of nitrogen and oxygen. Other gases belonging to this group are nitrogen monoxide and nitrogen pentoxide. Nitrogen dioxide is produced for the manufacture of nitric acid.

Complete answer:
For the kind of question here, we have to go through all the options in order to check whether the nitrogen $(I)$ oxide is produced or not.
Thermal decomposition of ammonium nitrate
$N{H_4}N{O_3} \to {N_2}O + 2{H_2}O$
Oxidation state of nitrogen in ${N_2}O$ is $ + 1$
Disproportion of ${N_2}{O_4}$
Gives nitrous acid and nitric acid like as follows,
${N_2}{O_4} + {H_2}O \to HN{O_2} + HN{O_3}$
Oxidation state of nitrogen in $HN{O_2}$ and $HN{O_3}$ are respectively $ + 3$ and $ + 5$
Thermal decomposition of ammonium nitrite
Gives out di nitrogen molecules and water
$N{H_4}N{O_2}(s) \to {N_2}(g) + 2{H_2}O(g)$
Oxidation state of nitrogen in ${N_2}$ is $0$
Interaction of hydroxylamine and nitrous acid
Gives out the following substances: $NaCl + 2{N_2}O + 2{H_2}O$
$N{H_2}OH + HN{O_2} \to {H_2}{N_2}{O_2} + {H_2}O$
Oxidation state of nitrogen in ${H_2}{N_2}{O_2}$ is $ + 1$
Hence when we look at that above elaborated solution from each and every option it is very clear that nitrogen oxide is produced by (A) thermal decomposition of ammonium nitrate and (D) interaction of hydroxylamine and nitrous acid.

Hence, the right options are (A) and (D).

Note: questions like this require to look into the options for a clear picture or the right option. These kinds of questions need a lot of time as we have to look into all the options and solve it until we know what is right for the answer part. This requires to look into the equation and to look into the oxidation state. The key is to learn the concept well and understanding of each and every step is important. Hence following all this makes it easy for attaining solutions.